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Persistent homology for low-complexity models
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Lotz, Martin (2019) Persistent homology for low-complexity models. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 475 (2230). doi:10.1098/rspa.2019.0081 ISSN 1364-5021.
An open access version can be found in:
Official URL: https://doi.org/10.1098/rspa.2019.0081
Abstract
We show that recent results on randomized dimension reduction schemes that exploit structural properties of data can be applied in the context of persistent homology. In the spirit of compressed sensing, the dimension reduction is determined by the Gaussian width of a structure associated to the data set, rather than its size, and such a reduction can be computed efficiently. We further relate the Gaussian width to the doubling dimension of a finite metric space, which appears in the study of the complexity of other methods for approximating persistent homology. We can therefore literally replace the ambient dimension by an intrinsic notion of dimension related to the structure of the data.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Journal or Publication Title: | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences | ||||||
Publisher: | The Royal Society Publishing | ||||||
ISSN: | 1364-5021 | ||||||
Official Date: | 2 October 2019 | ||||||
Dates: |
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Volume: | 475 | ||||||
Number: | 2230 | ||||||
DOI: | 10.1098/rspa.2019.0081 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||
Copyright Holders: | © 2019 The Author(s) | ||||||
Description: | Free access as of 2 October 2019 |
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